Fundamental Solution for Cauchy Initial Value Problem for Parabolic PDEs with Discontinuous Unbounded First-Order Coefficient at the Origin. Extension of the Classical Parametrix Method

Maria Rosaria Formica; Eugeny Ostrovsky; Leonid Sirota

doi:10.1007/s10440-020-00339-5

Fundamental Solution for Cauchy Initial Value Problem for Parabolic PDEs with Discontinuous Unbounded First-Order Coefficient at the Origin. Extension of the Classical Parametrix Method

Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota

Department of Mathematics

University of Naples Parthenope

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish also non-asymptotic, rapidly decreasing at infinity, upper and lower estimates for the fundamental solution. We extend the classical parametrix method of E.E. Levi.

Original language	English
Pages (from-to)	399-413
Number of pages	15
Journal	Acta Applicandae Mathematicae
Volume	170
Issue number	1
DOIs	https://doi.org/10.1007/s10440-020-00339-5
State	Published - 1 Dec 2020

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature B.V.

Funding

The first author has been partially supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Università degli Studi di Napoli Parthenope through the project “sostegno alla Ricerca individuale”. The first author has been partially supported by the Gruppo Nazionale per l?Analisi Matematica, la Probabilit? e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Universit? degli Studi di Napoli Parthenope through the project ?sostegno alla Ricerca individuale?.

Funders	Funder number
GNAMPA
Universit?
Istituto Nazionale di Alta Matematica "Francesco Severi"
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
Università degli Studi di Napoli Parthenope
Seconda Università degli Studi di Napoli

Keywords

Chapman-Kolmogorov equation
Fundamental solution
Generalized Mittag-Leffler function
Neumann series
Partial Differential Equation of parabolic type
Volterra’s integral equation

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10.1007/s10440-020-00339-5

Cite this

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Fundamental Solution for Cauchy Initial Value Problem for Parabolic PDEs with Discontinuous Unbounded First-Order Coefficient at the Origin. Extension of the Classical Parametrix Method. / Formica, Maria Rosaria; Ostrovsky, Eugeny; Sirota, Leonid.
In: Acta Applicandae Mathematicae, Vol. 170, No. 1, 01.12.2020, p. 399-413.

Research output: Contribution to journal › Article › peer-review

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KW - Neumann series

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Fundamental Solution for Cauchy Initial Value Problem for Parabolic PDEs with Discontinuous Unbounded First-Order Coefficient at the Origin. Extension of the Classical Parametrix Method

Abstract

Bibliographical note

Funding

Keywords

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